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The growth rate of real GDP per hour of work and the growth rate of capital per hour of work are each 3 percent per year. What percentage of productivity growth is due to technological change? (Round your answer to the nearest whole percent.)

Question

The growth rate of real GDP per hour of work and the growth rate of capital per hour of work are each 3 percent per year. What percentage of productivity growth is due to technological change? (Round your answer to the nearest whole percent.)

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Solution

To answer this question, we need to use the Cobb-Douglas production function, which states that output (Y) is a function of total factor productivity (A), capital (K), labor (L), and the shares of capital and labor in output (α and 1-α, respectively). The equation is as follows:

Y = A * K^α * L^(1-α)

The growth rate of output per hour of work (i.e., productivity) is the sum of the growth rate of total factor productivity, the share of capital times the growth rate of capital per hour of work, and the share of labor times the growth rate of labor per hour of work.

Given that the growth rate of real GDP per hour of work (productivity) and the growth rate of capital per hour of work are each 3 percent per year, we can set up the following equation:

0.03 = growth rate of A + α*0.03 + (1-α)*0.03

Solving for the growth rate of A (technological change), we get:

growth rate of A = 0.03 - α*0.03 - (1-α)*0.03

Assuming that the shares of capital and labor in output are equal (α = 0.5), we can simplify the equation to:

growth rate of A = 0.03 - 0.50.03 - 0.50.03 = 0

Therefore, 0 percent of productivity growth is due to technological change. However, this answer is based on the assumption that the shares of capital and labor in output are equal. If the shares are different, the percentage of productivity growth due to technological change would also be different.

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